The new model of dark matter reactivity hopefully can provide sufficient evidence, this will put to rest the age-old debate on the existence of antimatter.
Meaning: The new model of dark matter reactivity can, it is hoped, provide sufficient evidence to put to rest the age-old debate on the existence of antimatter.
We can easily eliminate A for joining two main clauses with just a comma to create a run-on sentence.
On the grounds of meaning,
will is not appropriate in the context of this sentence. Apart from expressing that something will happen in the future based on certain conditions,
will also express certainty. Meanwhile hopefully also expresses hope amidst some level of doubt pertaining to the occurrence of some event. Can is more appropriate when some level of doubt exists within the context of the sentence. Hence, hopefully works better with
can than
will agrees with hopefully. Based on this I can eliminate D.
On the same grounds of meaning, it doesn't make much sense to say that Dark matter hopes to put to rest the age-old debate. Does dark matter has what it takes to hope? Or is it that someone hopes that dark can[probably] provide sufficient evidence to put to rest the age-old debate on the existence of antimatter. For this illogical meaning, E can be eliminated.
In B we have dark matter can provide sufficient evidence that will put to rest the age-old debate. Already, can provide expresses some level of uncertainty. Something that is uncertain cannot form the basis for making categoric claims that evidence will put to rest the age-old debate. The infinitive form to put rather than will put as in C is better and sensical. With the infinitive, we can say that dark matter can provide sufficient evidence [
in order or
with the purpose] to put to rest the age-old debate. Eliminate B.
Now I'm left with option C. I hope my analysis has not taken a wrong turn to the North Pole; since we are in the season of Christmas

.
A) The new model of dark matter reactivity hopefully can provide sufficient evidence
, this will put to rest the age-old debate on the existence of antimatter.B) The new model of dark matter reactivity, it is hoped, can provide sufficient evidence
that will put to rest the age-old debate on the existence of antimatter.
C) The new model of dark matter reactivity can, it is hoped,
provide sufficient evidence
to put to rest the age-old debate on the existence of antimatter.
D) The new model of dark matter reactivity hopefully
will put to rest the age-old debate on the existence of antimatter.
E) The
new model of dark matter reactivity hopes to put to rest the age-old debate on the existence of antimatter.